Structural Assignments and Dynamics of the A Substates of MbCO: Spectrally Resolved Vibrational Echo Experiments and Molecular Dynamics Simulations

Neuroglobin dynamics observed with ultrafast 2D-IR vibrational echo spectroscopy

Neuroglobin (Ngb), a protein in the globin family, is found in vertebrate brains. It binds oxygen reversibly. Compared with myoglobin (Mb), the amino acid sequence has limited similarity, but key residues around the heme and the classical globin fold are conserved in Ngb. The CO adduct of Ngb displays two CO absorption bands in the IR spectrum, referred to as N(3) (distal histidine in the pocket) and N(0) (distal histidine swung out of the pocket), which have absorption spectra that are almost identical with the Mb mutants L29F and H64V, respectively. The Mb mutants mimic the heme pocket structures of the corresponding Ngb conformers. The equilibrium protein dynamics for the CO adduct of Ngb are investigated by using ultrafast 2D-IR vibrational echo spectroscopy by observing the CO vibration's spectral diffusion (2D-IR spectra time dependence) and comparing the results with those for the Mb mutants. Although the heme pocket structure and the CO FTIR peak positions of Ngb are similar to those of the mutant Mb proteins, the 2D-IR results demonstrate that the fast structural fluctuations of Ngb are significantly slower than those of the mutant Mbs. The results may also provide some insights into the nature of the energy landscape in the vicinity of the folded protein free energy minimum.

Viscosity-dependent protein dynamics

Spectrally resolved stimulated vibrational echo spectroscopy is used to investigate the dependence of fast protein dynamics on bulk solution viscosity at room temperature in four heme proteins: hemoglobin, myoglobin, a myoglobin mutant with the distal histidine replaced by a valine (H64V), and a cytochrome c552 mutant with the distal methionine replaced by an alanine (M61A). Fructose is added to increase the viscosity of the aqueous protein solutions over many orders of magnitude. The fast dynamics of the four globular proteins were found to be sensitive to solution viscosity and asymptotically approached the dynamical behavior that was previously observed in room temperature sugar glasses. The viscosity-dependent protein dynamics are analyzed in the context of a viscoelastic relaxation model that treats the protein as a deformable breathing sphere. The viscoelastic model is in qualitative agreement with the experimental data but does not capture sufficient system detail to offer a quantitative description of the underlying fluctuation amplitudes and relaxation rates. A calibration method based on the near-infrared spectrum of water overtones was constructed to accurately determine the viscosity of small volumes of protein solutions.

Ultrafast dynamics of myoglobin without the distal histidine: stimulated vibrational echo experiments and molecular dynamics simulations

Ultrafast protein dynamics of the CO adduct of a myoglobin mutant with the polar distal histidine replaced by a nonpolar valine (H64V) have been investigated by spectrally resolved infrared stimulated vibrational echo experiments and molecular dynamics (MD) simulations. In aqueous solution at room temperature, the vibrational dephasing rate of CO in the mutant is reduced by approximately 50% relative to the native protein. This finding confirms that the dephasing of the CO vibration in the native protein is sensitive to the interaction between the ligand and the distal histidine. The stimulated vibrational echo observable is calculated from MD simulations of H64V within a model in which vibrational dephasing is driven by electrostatic forces. In agreement with experiment, calculated vibrational echoes show slower dephasing for the mutant than for the native protein. However, vibrational echoes calculated for H64V do not show the quantitative agreement with measurements demonstrated previously for the native protein.

Molecular Dynamics Simulations of CN− Dynamics and Spectroscopy in Myoglobin

The vibrational dynamics of the cyanide anion and the heme group in MbCN (CN complexed to Myoglobin) are investigated using molecular dynamics simulations. A previously calculated quantum-chemical heme-ligand potential-energy surface together with a three-center charge model for the iron-ligand center that captures both polarization and ligand-to-metal charge transfer allows for a detailed description of the interactions around the active site. It is found that the CN binding orientation (Fe--CN or Fe--NC) to the heme affects the stretching frequency of the ligand, with a 25 cm-1 difference in the fundamental wavenumber between the two orientations as well as a change in bond length. The charge model also captures such crucial interactions as the possible hydrogen bond between the ligand and the His64 residue. This interaction is weakened when the ligand binds in the Fe--NC conformation but is also sensitive to the protonation state of His64. The structural changes around the active site, the observation of water penetration for the Fe--NC conformation, the computed IR spectrum, and the energetics suggest that the Fe--CN conformation with Hisepsilon64 is the most likely one. The water accessibility of the active site is also found to be related to the protonation state of His64. The presence of water in the active site could also affect the IR band of the C--N stretch mode. Thus, IR spectroscopy of the C--N stretch is a potentially useful reporter of ligand isomers and active-site structure.

Probing dynamics of complex molecular systems with ultrafast 2D IR vibrational echo spectroscopy

Ultrafast 2D IR vibrational echo spectroscopy is described and a number of experimental examples are given. Details of the experimental method including the pulse sequence, heterodyne detection, and determination of the absorptive component of the 2D spectrum are outlined. As an initial example, the 2D spectrum of the stretching mode of CO bound to the protein myoglobin (MbCO) is presented. The time dependence of the 2D spectrum of MbCO, which is caused by protein structural evolution, is presented and its relationship to the frequency-frequency correlation function is described and used to make protein structural assignments based on comparisons to molecular dynamics simulations. The 2D vibrational echo experiments on the protein horseradish peroxidase are presented. The time dependence of the 2D spectra of the enzyme in the free form and with a substrate bound at the active site are compared and used to examine the influence of substrate binding on the protein's structural dynamics. The application of 2D vibrational echo spectroscopy to the study of chemical exchange under thermal equilibrium conditions is described. 2D vibrational echo chemical exchange spectroscopy is applied to the study of formation and dissociation of organic solute-solvent complexes and to the isomerization around a carbon-carbon single bond of an ethane derivative.

Classical and quantum mechanical infrared echoes from resonantly coupled molecular vibrations

The nonlinear response function associated with the infrared vibrational echo is calculated for a quantum mechanical model of resonantly coupled, anharmonic oscillators at zero temperature. The classical mechanical response function is determined from the quantum response function by setting variant Planck's over 2pi-->0, permitting the comparison of the effects of resonant vibrational coupling among an arbitrary number of anharmonic oscillators on quantum and classical vibrational echoes. The quantum response function displays a time dependence that reflects both anharmonicity and resonant coupling, while the classical response function depends on anharmonicity only through a time-independent amplitude, and shows a time dependence controlled only by the resonant coupling. In addition, the classical response function grows without bound in time, a phenomenon associated with the nonlinearity of classical mechanics, and absent in quantum mechanics. This unbounded growth was previously identified in the response function for a system without resonant vibrational energy transfer, and is observed to persist in the presence of resonant coupling among vibrations. Quantitative agreement between classical and quantum response functions is limited to a time scale of duration inversely proportional to the anharmonicity.

Ultrafast 2D IR vibrational echo spectroscopy

The experimental technique and applications of ultrafast two-dimensional infrared (2D IR) vibrational echo spectroscopy are presented. Using ultrashort infrared pulses and optical heterodyne detection to provide phase information, unique information can be obtained about the dynamics, interactions, and structures of molecular systems. The form and time evolution of the 2D IR spectrum permits examination of processes that cannot be studied with linear infrared absorption experiments. Three examples are given: organic solute-solvent complex chemical exchange, dynamics of the hydrogen-bond network of water, and assigning peaks in an IR spectrum of a mixture of species.

Energetics and Dynamics in MbCN: CN--Vibrational Relaxation from Molecular Dynamics Simulations

The dynamics of the cyanide anion bound to sperm-whale myoglobin is investigated using atomistic simulations. With density-functional theory, a 2D potential energy surface for the cyanide-heme complex is calculated. Two deep minima with a stabilization energy of approximately 50 kcal/mol corresponding to two different binding orientations (Fe-CN and Fe-NC) of the ligand are found. The Fe-CN conformation is favored over Fe-NC by several kcal/mol. Mixed quantum mechanics/molecular mechanics calculations show that the binding orientation affects the bond strength of the ligand, with a significantly different bond length and a 25 cm-1 shift in the fundamental CN-frequency. For the molecular dynamics (MD) simulations, a 3-center fluctuating charge model for the Fe-CN unit is developed that captures polarization and ligand-metal charge transfer. Stability arguments based on the energetics around the active site and the CN- frequency shifts suggest that the Fe-CN conformation with epsilon-protonation of His epsilon 64 are most likely, which is in agreement with experiment. Both equilibrium and nonequilibrium MD simulations are carried out to investigate the relaxation time scale and possible relaxation pathways in bound MbCN. The nonequilibrium MD simulations with a vibrationally excited ligand reveal that vibrational relaxation takes place on a time scale of hundreds of picoseconds within the active site. This finding supports the hypothesis that the experimentally observed relaxation rate (3.6 ps) reflects the repopulation of the electronic ground state.

Cytochrome c552 Mutants: Structure and Dynamics at the Active Site Probed by Multidimensional NMR and Vibration Echo Spectroscopy

Spectrally resolved infrared stimulated vibrational echo experiments are used to measure the vibrational dephasing of a CO ligand bound to the heme cofactor in two mutated forms of the cytochrome c552 from Hydrogenobacter thermophilus. The first mutant (Ht-M61A) is characterized by a single mutation of Met61 to an Ala (Ht-M61A), while the second variant is doubly modified to have Gln64 replaced by an Asn in addition to the M61A mutation (Ht-M61A/Q64N). Multidimensional NMR experiments determined that the geometry of residue 64 in the two mutants is consistent with a non-hydrogen-bonding and hydrogen-bonding interaction with the CO ligand for Ht-M61A and Ht-M61A/Q64N, respectively. The vibrational echo experiments reveal that the shortest time scale vibrational dephasing of the CO is faster in the Ht-M61A/Q64N mutant than that in Ht-M61A. Longer time scale dynamics, measured as spectral diffusion, are unchanged by the Q64N modification. Frequency-frequency correlation functions (FFCFs) of the CO are extracted from the vibrational echo data to confirm that the dynamical difference induced by the Q64N mutation is primarily an increase in the fast (hundreds of femtoseconds) frequency fluctuations, while the slower (tens of picoseconds) dynamics are nearly unaffected. We conclude that the faster dynamics in Ht-M61A/Q64N are due to the location of Asn64, which is a hydrogen bond donor, above the heme-bound CO. A similar difference in CO ligand dynamics has been observed in the comparison of the CO derivative of myoglobin (MbCO) and its H64V variant, which is caused by the difference in axial residue interactions with the CO ligand. The results suggest a general trend for rapid ligand vibrational dynamics in the presence of a hydrogen bond donor.

Dynamics of proteins encapsulated in silica sol-gel glasses studied with IR vibrational echo spectroscopy

Spectrally resolved infrared stimulated vibrational echo spectroscopy is used to measure the fast dynamics of heme-bound CO in carbonmonoxy-myoglobin (MbCO) and -hemoglobin (HbCO) embedded in silica sol-gel glasses. On the time scale of approximately 100 fs to several picoseconds, the vibrational dephasing of the heme-bound CO is measurably slower for both MbCO and HbCO relative to that of aqueous protein solutions. The fast structural dynamics of MbCO, as sensed by the heme-bound CO, are influenced more by the sol-gel environment than those of HbCO. Longer time scale structural dynamics (tens of picoseconds), as measured by the extent of spectral diffusion, are the same for both proteins encapsulated in sol-gel glasses compared to that in aqueous solutions. A comparison of the sol-gel experimental results to viscosity-dependent vibrational echo data taken on various mixtures of water and fructose shows that the sol-gel-encapsulated MbCO exhibits dynamics that are the equivalent of the protein in a solution that is nearly 20 times more viscous than bulk water. In contrast, the HbCO dephasing in the sol-gel reflects only a 2-fold increase in viscosity. Attempts to alter the encapsulating pore size by varying the molar ratio of silane precursor to water (R value) used to prepare the sol-gel glasses were found to have no effect on the fast or steady-state spectroscopic results. The vibrational echo data are discussed in the context of solvent confinement and protein-pore wall interactions to provide insights into the influence of a confined environment on the fast structural dynamics experienced by a biomolecule.

Two-dimensional Raman spectra of atomic solids and liquids

We calculate third- and fifth-order Raman spectra of simple atoms interacting through a soft-core potential by means of molecular-dynamics (MD) simulations. The total polarizability of molecules is treated by the dipole-induced dipole model. Two- and three-body correlation functions of the polarizability at various temperatures are evaluated from equilibrium MD simulations based on a stability matrix formulation. To analyze the processes involved in the spectroscopic measurements, we divide the fifth-order response functions into symmetric and antisymmetric integrated response functions; the symmetric one is written as a simple three-body correlation function, while the antisymmetric one depends on a stability matrix. This analysis leads to a better understanding of the time scales and molecular motions that govern the two-dimensional (2D) signal. The 2D Raman spectra show novel differences between the solid and liquid phases, which are associated with the decay rates of coherent motions. On the other hand, these differences are not observed in the linear Raman spectra.

Multidimensional infrared spectroscopy for molecular vibrational modes with dipolar interactions, anharmonicity, and nonlinearity of dipole moments and polarizability

We present an analytical expression for the linear and nonlinear infrared spectra of interacting molecular vibrational motions. Each of the molecular modes is explicitly represented by a classical damped oscillator on an anharmonic multidimensional potential-energy surface. The two essential interactions, the dipole-dipole (DD) and the dipole-induced-dipole (DID) interactions, are taken into account, and each dipole moment and polarizability are expanded to nonlinear order with respect to the nuclear vibrational coordinate. Our analytical treatment leads to expressions for the contributions of anharmonicity, DD and DID interactions, and the nonlinearity of dipole moments and polarizability elements to the one-, two-, and three-dimensional spectra as separated terms, which allows us to discuss the relative importance of these respective contributions. We can calculate multidimensional signals for various configurations of molecules interacting through DD and DID interactions for different material parameters over the whole range of frequencies. We demonstrate that contributions from the DD and DID interactions and anharmonicity are separately detectable through the third-order three-dimensional IR spectroscopy, whereas they cannot be distinguished from each other in either the linear or the second-order IR spectroscopies. The possibility of obtaining the intra- or intermolecular structural information from multidimensional spectra is also discussed.

The Influence of Aqueous versus Glassy Solvents on Protein Dynamics: Vibrational Echo Experiments and Molecular Dynamics Simulations

Spectrally resolved infrared stimulated vibrational echo measurements are used to measure the vibrational dephasing of the CO stretching mode of carbonmonoxy-hemoglobin (HbCO), a myoglobin mutant (H64V), and a bacterial cytochrome c(552) mutant (Ht-M61A) in aqueous solution and trehalose glasses. The vibrational dephasing of the heme-bound CO is significantly slower for all three proteins embedded in trehalose glasses compared to that of aqueous protein solutions. All three proteins exhibit persistent but notably slower spectral diffusion when the protein surface is fixed by the glassy solvent. Frequency-frequency correlation functions (FFCFs) of the CO are extracted from the vibrational echo data to reveal that the structural dynamics, as sensed by the CO, of the three proteins in trehalose and aqueous solution are dominated by fast (tens of femtoseconds), motionally narrowed fluctuations. MD simulations of H64V in dynamic and "static" water are presented as models of the aqueous and glassy environments. FFCFs are calculated from the H64V simulations and qualitatively reproduce the important features of the experimentally extracted FFCFs. The suppression of long time scale (picoseconds to tens of picoseconds) frequency fluctuations (spectral diffusion) in the glassy solvent is the result of a damping of atomic displacements throughout the protein structure and is not limited to structural dynamics that occur only at the protein surface. The analysis provides evidence that some dynamics are coupled to the hydration shell of water, supporting the idea that the bioprotection offered by trehalose is due to its ability to immobilize the protein surface through a thin, constrained layer of water.

Multidimensional vibrational spectroscopy for tunneling processes in a dissipative environment

Simulating tunneling processes as well as their observation are challenging problems for many areas. In this study, we consider a double-well potential system coupled to a heat bath with a linear-linear (LL) and square-linear (SL) system-bath interactions. The LL interaction leads to longitudinal (T1) and transversal (T2) homogeneous relaxations, whereas the SL interaction leads to the inhomogeneous dephasing (T2*) relaxation in the white noise limit with a rotating wave approximation. We discuss the dynamics of the double-well system under infrared (IR) laser excitations from a Gaussian-Markovian quantum Fokker-Planck equation approach, which was developed by generalizing Kubo's stochastic Liouville equation. Analytical expression of the Green function is obtained for a case of two-state-jump modulation by performing the Fourier-Laplace transformation. We then calculate a two-dimensional infrared signal, which is defined by the four-body correlation function of optical dipole, for various noise correlation time, system-bath coupling parameters, and temperatures. It is shown that the bath-induced vibrational excitation and relaxation dynamics between the tunneling splitting levels can be detected as the isolated off-diagonal peaks in the third-order two-dimensional infrared (2D-IR) spectroscopy for a specific phase matching condition. Furthermore, this spectroscopy also allows us to directly evaluate the rate constants for tunneling reactions, which relates to the coherence between the splitting levels; it can be regarded as a novel technique for measuring chemical reaction rates. We depict the change of reaction rates as a function of system-bath coupling strength and a temperature through the 2D-IR signal.

Dynamics of hemoglobin in human erythrocytes and in solution: influence of viscosity studied by ultrafast vibrational echo experiments

Ultrafast spectrally resolved stimulated vibrational echo experiments are used to measure the vibrational dephasing of the CO stretching mode of hemoglobin-CO (HbCO) inside living human erythrocytes (red blood cells), in liquid solutions, and in a glassy matrix. A method is presented to overcome the adverse impact on the vibrational echo signal from the strong light scattering caused by the cells. The results from the cytoplasmic HbCO are compared to experiments on aqueous HbCO samples prepared in different buffers, solutions containing low and high concentrations of glycerol, and in a solid trehalose matrix. Measurements are also presented that provide an accurate determination of the viscosity at the very high Hb concentration that is found inside the cells. It is demonstrated that the dynamics of the protein, as sensed by the CO ligand, are the same inside the erythrocytes and in aqueous solution and are independent of the viscosity. In solutions that are predominantly glycerol, the dynamics are modified somewhat but are still independent of viscosity. The experiments in trehalose give the dynamics at infinite viscosity and are used to separate the viscosity-dependent dynamics from the viscosity-independent dynamics. Although the HbCO dynamics are the same in the red blood cell and in the equivalent aqueous solutions, differences in the absorption spectra show that the distribution of a protein's equilibrium substates is sensitive to small pH differences.

Vibrational energy relaxation in proteins

An overview of theories related to vibrational energy relaxation (VER) in proteins is presented. VER of a selected mode in cytochrome c is studied by using two theoretical approaches. One approach is the equilibrium simulation approach with quantum correction factors, and the other is the reduced model approach, which describes the protein as an ensemble of normal modes interacting through nonlinear coupling elements. Both methods result in similar estimates of the VER time (subpicoseconds) for a CD stretching mode in the protein at room temperature. The theoretical predictions are in accord with previous experimental data. A perspective on directions for the detailed study of time scales and mechanisms of VER in proteins is presented.

Ligand Dynamics in Myoglobin: Calculation of Infrared Spectra for Photodissociated NO

We present molecular dynamics simulations of the photodissociated state of MbNO performed at 300 K using a fluctuating charge model for the nitric oxide (NO) ligand. After dissociation, NO is observed to remain mainly in the centre of the distal haem pocket, although some movement towards the primary docking site and the xenon-4 pocket can be seen. We calculate the NO infrared spectrum for the photodissociated ligand within the haem pocket and find a narrow peak in the range 1915-1922 cm(-1). The resulting blue shift of 1 to 8 cm(-1) compared to gas-phase NO is much smaller than the red shifts calculated and observed for carbon monoxide (CO) in Mb. A small splitting, due to NO in the xenon-4 pocket, is also observed. At lower temperatures, the spectra and conformational space explored by the ligand remain largely unchanged, but the electrostatic interactions with residue His64 become increasingly significant in determining the details of the ligand orientation within the distal haem pocket. The investigation of the effect of the L29F mutation reveals significant differences between the behaviour of NO and that of CO, and suggests a coupling between the ligand and the protein dynamics due to the different ligand dipole moments.

Interpreting nonlinear vibrational spectroscopy with the classical mechanical analogs of double-sided Feynman diagrams

Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.

Semiclassical calculation of the vibrational echo

The infrared echo measurement probes the time scales of the molecular motions that couple to a vibrational transition. Computation of the echo observable within rigorous quantum mechanics is problematic for systems with many degrees of freedom, motivating the development of semiclassical approximations to the nonlinear optical response. We present a semiclassical approximation to the echo observable, based on the Herman-Kluk propagator. This calculation requires averaging over a quantity generated by two pairs of classical trajectories and associated stability matrices, connected by a pair of phase-space jumps. Quantum, classical, and semiclassical echo calculations are compared for a thermal ensemble of noninteracting anharmonic oscillators. The semiclassical approach uses input from classical mechanics to reproduce the significant features of a complete, quantum mechanical calculation of the nonlinear response.

Two-dimensional Raman and infrared vibrational spectroscopy for a harmonic oscillator system nonlinearly coupled with a colored noise bath

Multidimensional vibrational response functions of a harmonic oscillator are reconsidered by assuming nonlinear system-bath couplings. In addition to a standard linear-linear (LL) system-bath interaction, we consider a square-linear (SL) interaction. The LL interaction causes the vibrational energy relaxation, while the SL interaction is mainly responsible for the vibrational phase relaxation. The dynamics of the relevant system are investigated by the numerical integration of the Gaussian-Markovian Fokker-Planck equation under the condition of strong couplings with a colored noise bath, where the conventional perturbative approach cannot be applied. The response functions for the fifth-order nonresonant Raman and the third-order infrared (or equivalently the second-order infrared and the seventh-order nonresonant Raman) spectra are calculated under the various combinations of the LL and the SL coupling strengths. Calculated two-dimensional response functions demonstrate that those spectroscopic techniques are very sensitive to the mechanism of the system-bath couplings and the correlation time of the bath fluctuation. We discuss the primary optical transition pathways involved to elucidate the corresponding spectroscopic features and to relate them to the microscopic sources of the vibrational nonlinearity induced by the system-bath interactions. Optical pathways for the fifth-order Raman spectroscopies from an "anisotropic" medium were newly found in this study, which were not predicted by the weak system-bath coupling theory or the standard Brownian harmonic oscillator model.

Myoglobin-CO substate structures and dynamics: multidimensional vibrational echoes and molecular dynamics simulations

Spectrally resolved infrared stimulated vibrational echo data were obtained for sperm whale carbonmonoxymyoglobin (MbCO) at 300 K. The measured dephasing dynamics of the CO ligand are in agreement with dephasing dynamics calculated with molecular dynamics (MD) simulations for MbCO with the residue histidine-64 (His64) having its imidazole epsilon nitrogen protonated (N(epsilon)-H). The two conformational substate structures B(epsilon) and R(epsilon) observed in the MD simulations are assigned to the spectroscopic A(1) and A(3) conformational substates of MbCO, respectively, based on the agreement between the experimentally measured and calculated dephasing dynamics for these substates. In the A(1) substate, the N(epsilon)-H proton and N(delta) of His64 are approximately equidistant from the CO ligand, while in the A(3) substate, the N(epsilon)-H of His64 is oriented toward the CO, and the N(delta) is on the surface of the protein. The MD simulations show that dynamics of His64 represent the major source of vibrational dephasing of the CO ligand in the A(3) state on both femtosecond and picosecond time scales. Dephasing in the A(1) state is controlled by His64 on femtosecond time scales, and by the rest of the protein and the water solvent on longer time scales.